Question

write a quadratic polynomial whose zeros are-3√2,√2.​

Answer 1

Answer :

x² + 2√2x - 6

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.

★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;

D = b² - 4ac

★ If D = 0 , then the zeros are real and equal .

★ If D > 0 , then the zeros are real and distinct .

★ If D < 0 , then the zeros are unreal (imaginary) .

Solution :

Given : Zeros = -3√2 , √2

To find : Quadratic polynomial

Here ,

The given zeros of the quadratic polynomial are -3√2 and √2 .

Thus ,

Let α = -3√2 and ß = √2

Now ,

Sum of zeros will be ;

α + ß = -3√2 + √2 = -2√2

Also ,

Product of zeros will be ;

αß = -3√2•√2 = -6

Now ,

The family of quadratic polynomials will be ;

=> k•[x² - (α + ß)x + αß]

=> k•[x² - (-2√2)x + (-6)]

=> k•[x² + 2√2x - 6]

For k = 1 , the Quadratic polynomial will be ;

x² + 2√2x - 6 .

Hence ,

Required quadratic polynomial is ;

x² + 2√2x - 6 .